J. Chem. SOC., Faraday Trans. I , 1982, 78, 1465-1472 Temperature Dependence and Diffusion Control of the Rate Constant for Energy Transfer from Decalin to Benzene BY GIORGIO ORLANDI,*-~ SERGIO DELLONTE, LUCIA FLAMIGNI AND FRANCESCO BARIGELLETTI Istituto di Fotochimica e Radiazioni d'Alta Energia del C.N.R., Via de'castagnoli I, 401 26 Bologna, Italy Received 18th May, 1981 The transfer of energy from decaiin to solute benzene has been studied in the temperature range -20 to + 57 "C. The quenching of decalin fluorescence by benzene has been monitored by performing both intensity and lifetime measurements. The temperature dependence of the quenching process is found to be consistent with a diffusion-controlled mechanism. An important source of information on the properties of the emitting excited state of saturated hydrocarbons is the study of kinetic parameters governing the quenching of their weak fluorescence.' In the last decade several experiments have been performed with the aim of measuring such parameter^.^.^ In most work, liquid alkanes containing suitable solutes at various concentrations were excited by means of ionizing radiation and the quenching of the fluorescence intensity of the alkane itself or the appearance and growth of the solute emission were monitored.The only experiment concerning the fluorescence lifetime quenching reported so far has been performed on a unique concentration of CCl, q ~ e n c h e r . ~ These experiments have shown that the emission intensities depend on the solute concentration according to the linear Stern-Volmer (SV) equation,6 at least for concentrations which are not too high, but surprisingly the SV rate parameter is one or two orders of magnitude larger than the value expected for diffusion-con t rolled processes. These results, suggesting that the emitting state has Rydberg character,' i.e. involving the excitation of one electron from a valence to a higher shell diffuse orbital, are in our opinion open to question as they could be influenced by the concomitant transient dynamic quenching effecta and by ionic reactions deriving from the high-energy ex~itation.~ To obtain information free of such spurious effects, we performed quenching experiments on both the lifetime and the intensity of the alkane fluorescence using a two-photon excitation produced by a nitrogen laser.l0 The corresponding wavelength is 168.5 nm, which is slightly above the onset of the absorbtion spectra of most saturated hydrocarbons and is thus not expected to produce ionization.The quenching rate constants obtained with this procedure for the system decalin- benzene and cyclohexane-benzene, at room temperature, are compatible with diffus- ional processes.ll We have now studied the temperature dependence of the quenching rate parameter of the system decalin-benzene in order to ascertain whether additional support can be found for our previous conclusions. t Permanent address : Istituto Chimico 'G. Ciamician', Universita di Bologna, Bologna, Italy. 1465 48 FAR 11466 ENERGY TRANSFER FROM DECALIN TO BENZENE EXPERIMENTAL Decalin (Baker, Analysed Reagent) was passed twice through a 50cm column of freshly activated silica gel; the purity was spectroscopically controlled.The cis: trans molar ratio of the decalin used was determined by viscometric measurements, taking the viscosity data of ref. (12) as standard. The cis: trans molar ratio was found to be 2: 5. Thiophene-free benzene (Baker, Analysed Reagent) was used as purchased. All samples were sealed under vacuum after repeated freeze-pumpthaw cycles in 1 cm fluorescence cells. Benzene concentrations were determined spectroscopically. The excitation was obtained from a pulsed nitrogen laser (Lambda Physik, Gottingen) with a pulse width of ca. 3.5 ns and a pulse power of 1 MW. The beam was focussed on an area smaller than 0.05 cm2 where, as previously reported,1° a two-photon excitation of the alkane molecules took place.For fluorescence intensity measurements the exciting beam was focussed on the extreme edge of the cell to prevent reabsorption. The emission at 90' to the laser pulsca was detected using an R.C.A. 1P28 photomultiplier with a five-dinode chain configuration to obtain a faster time response. The emitted light was filtered by a 5 cm cell filled with C1, at a pressure of 2 atm* and a Bausch-Lomb high-intensity monochromator. Data were acquired and reduced using an R7912 Tektronix transient digitizer interfaced to a Z-2D Cromemco microcomputer. The deconvolution analysis of the fluorescence decay curves was performed by a non-linear iterative least-squares fitting procedure over stored couples of flash and decay curves, each partitioned in 256 data.points.With a sweep rate of 2 ns per division (full time-scale of 20 ns), the instrumental time resolution is ca. 0.080 ns. Further details on the experimental set up and deconvolution procedure are reported elsewhere.lO9 l1 Lifetime values were obtained by averaging two sets of five measurements each. The scattering (i.e. )zmitX - zminl) in z values for a given c and T was < 7%. The (1,JI) data were obtained from the ratio of integrated emission signals of pure decalin and benzene solutions; any reported value is the average of two sets of ten ( I o / I ) measurements. The spread in these data for a given c and T was < 10%. The errors relevant to z and ( I o / I ) are assumed to be respectively, The measurements at 0 and 20 OC were performed using an Air Products cryostatic apparatus.Above 0 O C temperatures were regulated by water flowing through the cell block. The absolute error in temperature measurements was & 0.5 "C. 5 % and & 7%. RESULTS The decay of decalin fluorescence for various concentrations of benzene was monitored at different temperatures in the range - 20 to + 57 O C . The detected signals could be deconvoluted with a satisfactory fitting, according to a single-exponential decay, yielding the fluorescence lifetime, z, of decalin. At each temperature z followed the SV equation which holds for a collisional irreversible energy-transfer process z-l = z,'+kc (1) where z, is the fluorescence lifetime of the pure solvent, k is the emission quenching parameter and c is the concentration of benzene.In fig. 1 typical examples of plots of z-l against c, for some of the temperatures considered, are shown. The values of k and z, obtained from the plots are listed in table 1. The value of zo at room temperature is in good agreement with previously found values.l39 l4 The small difference in the present k value at room temperature compared with our previous result" reflects the improved data acquisition procedure used in this work. From the data of table 1 it can be seen that both the magnitude of k and its temperature dependence are typical of diffusion-controlled processes. l4 * 1 atm = 101 325 PaG. ORLANDI, s. DELLONTE, L. FLAMIGNI AND F. BARIGELLETTI 1467 1 0 0 3 6 9 [benzene] / 1 0-2 mol dm-3 FIG.1 .-Quenching of decalin fluorescence lifetimes as a function of benzene concentration at various temperatures: 0, 253; a, 298; ., 330 K. TABLE 1 .-DECALIN FLUORESCENCE LIFETIMES, z,,, AND FLUORESCENCE QUENCHING PARAMETERS, k AND k', AT VARIOUS TEMPERATURES The estimated errors are & 5% for z, f 8% for k and f 13% for k'. T/"C k/dm3 mol-l s-I k'/dm3 mol-l s-l - 20 3 . 3 0 ~ 109 2.89 4.2x 109 0 4.05 x 109 2.86 4.3 x 109 + 15 4.41 x 109 2.40 3.5 x 109 + 25 4.91 x 109 2.36 3.8 x 109 + 35 6.35 x 109 2.30 4.1 x 109 + 45 7 . 1 7 ~ 109 2.24 4.0 x 109 + 57 7.99x 109 2.18 5.1 x 109 Parallel measurements of the intensity of decalin fluorescence, for various benzene concentrations, were performed. The fluorescence intensity, I, follows the SV equation I,/I = 1 +k,z,c only for low values of c, but shows an upward bend for large c, as noted previous1y.l' In eqn (2), I, represents the intensity of pure decalin and k, an appropriate emission intensity quenching parameter.Plots I,/I against c for several temperatures are reported in fig. 2. The values obtained for k , from the linear part of the plots (i.e. for c < mol dmW3) are ca. 50% larger than those obtained for k at the same temperature. The difference between the intensity and the lifetime plots can be understood in the framework of diffusion-controlled p r o c e ~ s e s ~ ~ ~ l5 in terms of the transient quenching effect.8* 16+ l7 This effect, which is important for emitters of short lifetime dissolved in a (highly) viscous solvent, is due to the almost instantaneous quenching of the emitter by the initially adjacent quencher molecules (i.e.without requiring diffusion). In the lifetime measurements the almost instantaneous non-exponential decay associated with the transient quenching effect tends to escape observation (at least if the time resolution is not very good) and is overshadowed by the longer, exponential decay 48-21468 0 ENERGY TRANSFER FROM DECALIN TO BENZENE 0 2 6 10 [benzene]/ 1 O-’ mol dm-3 FIG. 2.-Quenching of decalin fluorescence intensities as a function of benzene concentration at two temperatures: (a) 330, (b) 288 K. Dashed lines are calculated from eqn (2), using k , = k reported in table 1 . due to the diffusional process. In the intensity measurements, on the other hand, the transient dynamic quenching is fully manifest.This explains the difference in behaviour between lifetime and intensity quenching. The treatment of this effect has been given by Forster and Weller17 and, more recently, by Ware and coworkers.16 Given the resolution of our apparatus, the simpler formulae of ref. (17) have been used. According to these authors, the lifetime quenching, observed after the rapid transient quenching, is described by eqn (l), while the intensity quenching is given by I,/I = (1 + kz, C) exp [k’z, C( 1 + kz, c)-i] (3) where k’ is a parameter describing the transient dynamic quenching. The values for k’ can be derived by fitting the experimental results to eqn (3) and using the parameters z, and k determined with the lifetime experiments. The values of k’ obtained for the system decalin-benzene are given in table 1.As for the accuracy of these results, the values for k tend to be overestimated because they contain a contribution from the dynamic quenching, and conversely those for k’ are underestimated. These systematic errors are not considered to exceed the uncertainties on k and k’ (reported in table 1) which, however, are small enough to allow a discussion of the mechanism of the quenching.G . ORLANDI, S. DELLONTE, L. FLAMIGNI AND F. BARIGELLETTI 1469 DISCUSSION According to the theories for diffusion-controlled processes, k and k' can be expressed in term of diffusional parameters; specifically k is given by l5 k = 4nNRD ( 4 ) k' = kR(t,D)-i ( 5 ) and k' is related to k by17 where D = D , + D, is the sum of the diffusion coefficients of the emitter (solvent, S) and of the quencher (solute, s), R is the quenching distance or interaction radius and N' = 6.02 x 1020.* By solving eqn (4) and (9, values for D and R are obtained on the basis of the experimentally determined k and k'.These values, which are reported in table 2, are of the size expected for diffusion-controlled processes. TABLE z.-EXPERIMENTAL DIFFUSION COEFFICIENTS, Dexp., AND QUENCHING DISTANCES, R, AT VARIOUS TEMPERATURES The fourth column displays theoretical diffusion coefficients, Dtheor., calculated using eqn (7) and the values of the fifth column. The estimated errors are & 2 5 % for Dexp. and f 15% for R. 7.00 x - 20 3 x 1 3 2.2 x 3.88 x 0 4 x 10-6 1 2 4.3 x + 15 6 x 10 6.4 x 2.75 x + 25 7 x 1 0 8.2 x lov6 2.22 x + 3 5 9 x 10-6 9 1 0 .2 x 1.85 x lop2 + 4 5 1 1 x 9 12.5 x 1 . 5 7 x 1.31 x + 57 1 1 x 10 15.5 x Calculated by D = D,+D, and eqn (7); b, = 3.9 A and b, = 3.3 A. The interaction radius obtained falls in the range typical of collisional interactions (6-15 AT).16u In principle, an important contribution to the quenching of alkane fluorescence by benzene is associated with the singlet-singlet energy-transfer process. This is governed by dipole-dipole interactionslg and takes place over a critical transfer distance, Ro, usually in the order of 20-50 i.e. larger than the collisional distance. We have estimated R, for the present case, using the relationshipleb where, in keeping with the notation of ref. ( l s b ) , F,(v) is the donor fluorescence spectrum normalized to the fluorescence quantum yield, E,(v) is the molar decadic extinction coefficient of the quencher, n is the solvent refractive index and N is Avogadro's number.Using F, V ) taken from ref. (1) and cS($ measured in our radii. This rather low value for R, indicates that, in this case, the coulombic interaction laboratory, we obtain R, = 8.4 8, , which is the same size as the collisional interaction * When N' = 6.02 x lo2', D is in cm2 s-' and R in cm, the units of k and k' are dm3 mol-' SKI. t 1 A = 10-10 m = 10-1 nm.1470 ENERGY TRANSFER FROM DECALIN TO BENZENE is effective only at a short range, and the reason for this is the low fluorescence quantum yield of decalin and the rather poor overlap between the &(v) and E,(v) spectra.The diffusion coefficients D, and D,, according to the Stokes-Einstein (SE) theory,15 ( 7 ) are given by where k is Boltzmann’s constant, T is the absolute temperature, q is the solvent viscosity and b,, b, the Stokes (collision) radii. Eqn ( 7 ) is the modified form of the SE relationship, derived assuming that the coefficient of sliding friction is zero, which is appropriate for molecules of size comparable or smaller than those of the solvent.18C Using the values reported for the viscosity12 for the cis: trans molar ratio of decalin used, we derived the theoretical values of D, which are shown in table 2 along with the values of q used. The correlation between the values of the diffusion coefficients calculated by eqn (7) (theoretical) and those obtained by eqn ( 4 ) and ( 5 ) (experimental) is quite good as both are of the same size and increase at a similar rate with temperature.The ‘theoretical’ D grows faster with the temperature than its ‘experimental’ counterpart, but this is not unexpected. In fact, while according to eqn ( 7 ) the product Dq/ T should be constant, quite often it is found to depend on q (or on T ) . The following empirical equation14 Dq/T = A+bqx where x is an appropriate parameter, approximately 1, has been proposed to describe the experimental behaviour of D. The best fitting of our ‘experimental’ D to eqn (8) (see fig. 3) gives A = 3.4 x 10-lo cm2 P s-’ K-l, b = 8.6 x cm2 s-l K-I and x = 1. D , = kT/4xqb, D, = kT/4nqbS (8) 0 ~ 0.02 5 0.0 50 0.075 VIP FIG. 3.-Plot of Dq/T against q for benzene in decalin.The parameter A represents the Stokes-Einstein behaviour described by eqn (7) and b describes a deviation from it arising from the contribution to the motion of the solute molecules due to their spontaneous change of position as a result of their flow into the holes of the solvent. It can be seen that the value obtained for A is in fair agreement with the theoretical estimate of 6.1 x cm2 P s-l K-l, obtained from eqn (7) for the diffusion coefficient.G. ORLANDI, S. DELLONTE, L. FLAMIGNI A N D F. BARIGELLETTI 1471 CONCLUSION The quenching of decalin fluorescence by benzene solute, as a function of temperature, has been investigated by performing both intensity and kinetic measure- ments. The temperature dependence of the quenching process is found to be fully consistent with a diffusion controlled mechanism.In fact, analysing the experimental parameters k and k’ in terms of the diffusional process, one obtains a diffusion coefficient D with the proper size and temperature dependence. We believe this result remains valid if allowance is made for the approximations involved in obtaining k and k’. Different results obtained using high-energy excitation sources2 may be explained by the presence of species, such as alkane ions, which are known to yield excited states upon rec~mbination.~ Under such conditions the quenching of the donor fluorescence intensity as well as the growing of the acceptor emission may encompass both excited states and ionic processes. Furthermore, the use of quenchers having a large spectral overlap with the donor fluorescence could cause an efficient energy-transfer via dipole-dipole interactionIg with a rate constant larger than the diffusional one.This is a well known fact and it cannot be taken as suggestive of anomalous behaviour of the alkane singlet state. In conclusion, the fluorescence quenching of decalin by benzene takes place by a diffusion mechanism in agreement with our previous findings.ll This result indicates that the nature of the emitting excited state of decalin is that of a valence state rather than that of a Rydberg state.’ This indication is supported by the shape of the vibrational envelope of decalin fluorescence, which lacks the vibrational structure1 typical of Rydberg transitions. We thank L.Minghetti and G. Mancini for their technical assistance. W. Rothmans, F. Hirayama and S. Lipsky, J. Chem. Phys., 1973, 58, 1300. L. Walter and S. Lipsky, Int. J. Radiat. Phys. Chem., 1975, 7, 175. J. 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Chem., 1975, 41, 635.1472 ENERGY TRANSFER FROM DECALIN TO BENZENE l7 A. Weller, Prog. React. Kinet., 1961, 1, 187 ; Th. Forster, Fluorescenz Organischer Verbindungen (Vanderhoeck and Ruprecht, Gottingen, 195 1). J. B. Birks, Photophysics of Aromatic Molecules (Wiley Interscience, New York, 1970), ( a ) p. 518; (b) p. 569; ( c ) p. 511. l9 Th. Forster, Discuss. Faraday SOC., 1959, 27, 7. (PAPER 1 /798)